login
Number of indecomposable Type II binary self-dual codes of length 8n.
11

%I #15 Oct 04 2012 10:28:57

%S 1,1,1,7,75,94251

%N Number of indecomposable Type II binary self-dual codes of length 8n.

%D J. H. Conway and V. S. Pless, On the enumeration of self-dual codes, J. Comb. Theory, A28 (1980), 26-53.

%D V. S. Pless, The children of the (32,16) doubly even codes, IEEE Trans. Inform. Theory, 24 (1978), 738-746.

%H Koichi Betsumiya, Masaaki Harada and Akihiro Munemasa, <a href="http://arxiv.org/abs/1104.3727">A Complete Classification of Doubly Even Self-Dual Codes of Length 40</a>, arXiv:1104.3727v3 [math.CO], v3, Aug 02, 2012.

%H J. H. Conway, V. Pless and N. J. A. Sloane, The Binary Self-Dual Codes of Length Up to 32: A Revised Enumeration, J. Comb. Theory, A28 (1980), 26-53 (<a href="http://neilsloane.com/doc/pless.txt">Abstract</a>, <a href="http://neilsloane.com/doc/pless.pdf">pdf</a>, <a href="http://neilsloane.com/doc/pless.ps">ps</a>, <a href="http://neilsloane.com/doc/plesstaba.ps">Table A</a>, <a href="http://neilsloane.com/doc/plesstabd.ps">Table D</a>).

%H G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.

%H E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (<a href="http://neilsloane.com/doc/self.txt">Abstract</a>, <a href="http://neilsloane.com/doc/self.pdf">pdf</a>, <a href="http://neilsloane.com/doc/self.ps">ps</a>).

%Y Cf. A003178, A003179, A106163-A106167.

%K nonn,hard,more

%O 0,4

%A _N. J. A. Sloane_, May 09 2005

%E a(4) corrected by John van Rees, Jul 21 2005. It was given as 76 by Conway and Pless and as 74 by Rains and Sloane.

%E a(5) = 94251 = 94343 - 75 - 7 - 7 - 1 - 1 - 1 (cf. A106163) from Koichi Betsumaya, Aug 11 2012